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Will anyone ever have 20 consecutive winning seasons like the Dallas Cowboys did from 1966-1985? Given the parity in the league, I tend to doubt it. Maybe it could happen if you find a quarterback who can play for 20 years.
This list of consecutive winning seasons from volstedgridban is pretty cool. The Chiefs show up on the list twice -- 1965-1973 and again from 1989-1977. The Hank Stram years and the Marty years. Interestingly the Baltimore/Indianapolis Colts have a very similar history as the Chiefs with two separate streaks of nine consecutive winning seasons.
Check out the whole list here.
Consecutive
Winning
Seasons Seasons
Dallas Cowboys 20 1966 - 1985
Oakland Raiders 16 1965 - 1980
San Francisco 49ers 16 1983 - 1998
Chicago Bears 15 1930 - 1944
Green Bay Packers 14 1934 - 1947
Cleveland Browns 13 1957 - 1969
New England Patriots 12 2001 -
Washington Redskins 10 1936 - 1945
New York Giants 10 1954 - 1963
Detroit Lions 9 1931 - 1939
Pittsburgh Steelers 9 1972 - 1980
Kansas City Chiefs 9 1965 - 1973
1989 - 1997
Indianapolis Colts 9 1963 - 1971
2002 - 2010